1 / 25

What? A Math Class That is Not All Lecture?

What? A Math Class That is Not All Lecture? . Dr. Heidi Hansen Dr. Glen Richgels Bemidji State University. Overview. Common teaching practices Needs of students Change and standards recommendations Background/origins of the course Focus of the course Activity example

hammer
Download Presentation

What? A Math Class That is Not All Lecture?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. What? A Math Class That is Not All Lecture? Dr. Heidi Hansen Dr. Glen Richgels Bemidji State University

  2. Overview • Common teaching practices • Needs of students • Change and standards recommendations • Background/origins of the course • Focus of the course • Activity example • Impact of the course on algebra understanding • Student reactions to the class

  3. Teaching practices • Historically geared towards calculus as an entry level college course (Ganter & Barker, 2003) • Primarily lecture (Dossey, Halvorson, McCrone, 2008) • Separate courses for algebra, statistics, geometry, computer • Primarily skill-focused with some applications included in each section

  4. Today’s College Students • Blossoming growth in enrollment at 2 year colleges • Nearly 1,000,000 students taking courses below Calculus in the U.S. (Statistical Abstract Of Undergraduate Programs in the Mathematical Sciences in the U.S. Lutzer, 2005) • Up to 50% DWF rate in College Algebra at the college level (Baxter-Hastings, et. al, 2006) • Only 6% of two-year college students enrolled in Calculus (Lutzer, 2005)

  5. Today’s students (cont.) • Students who didn’t succeed in high school math generally don’t succeed in college math (Baxter Hastings, et al., 2006) • 57% of two-year college students are enrolled in remedial courses. (Lutzer, et al., 2005) • Needs of students have changed!

  6. CRAFTY study by CUPM-MAACurriculum Renewal Across the First Two Years Committee for the Undergraduate Program in Mathematics-MAA • Looked at partner disciplines needs in 11 workshops across the country • physical sciences, the life sciences, computer science, engineering, economics, business, education, and some social sciences • Math faculty just sat back and listened, answered questions • Published A Collective Vision: Voices of the Partner Disciplines (Ganter & Barker, 2003)

  7. Mathematical Needs of Other Disciplines • Conceptual understanding • Problem solving skills • Modeling • Communicating mathematically • Balance between mathematical perspectives

  8. Needs of other disciplines (cont.) Content: • Descriptive statistics • Real world applications of mathematics • 2 and 3-dimension and scale • Use of technology especially spreadsheets (Not more emphasis on algebraic manipulations)

  9. Pedagogical recommendations • Teaching methods for a variety of learning styles • Active learning • In-class problem solving • Class and group discussions • Collaborative group work • Out of class projects

  10. MAA’s CUPM Curriculum Guide (2004) Recommendations for Teaching Students Taking Minimum Requirements • Offer courses which • Engage students • Increase quantitative reasoning skills • Strengthen mathematical abilities applicable in other disciplines • Improve student communication of quantitative ideas • Encourage students to take more mathematics • Examine the effectiveness of College Algebra for meeting the needs of students • Examine whether students succeed in future coursework

  11. AMATYC Standards • Crossroads in Mathematics: Standards for Introductory College Mathematics (1995) • Beyond Crossroads: Implementing College Mathematics in the First Two Years of College (2006)

  12. Agreement in the documents(Baxter Hastings, et al., 2006) CONTENT: • Lessen the traditional amount of time performing algebraic manipulations; • Decrease time spent executing algorithms simply for the sake of calculation; • Restrict the topics covered to the most essential; • Decrease the amount of time spent lecturing; • Deemphasize rote skills and memorization of formulas.

  13. Agreement (cont.) PEDAGOGY: • Embed the mathematics in real life situations that are drawn from the other disciplines; • Explore fewer topics in greater depth; • Emphasize communication of mathematics through discussion and writing assignments; • Utilize group assignments and projects to enhance communication in the language of mathematics;

  14. Agreement (cont.) PEDAGOGY (cont.) • Use technology to enhance conceptual understanding of the mathematics; • Give greater priority to data analysis; • Emphasize verbal, symbolic, graphical, and written representations • Focus much more attention on the process of constructing mathematical models before finding solutions to these models.

  15. New: The Common Core Mathematical Practices • 1. Make sense of problems and persevere in solving them. • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 6. Attend to precision. • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning.

  16. Preparing students for college • Students are often not prepared for the mathematical needs of the college disciplines • High school needs should tie in to college needs • As noted before, students who do not succeed in high school math do not succeed in college math • What kind of a course do students need?

  17. Introduction to the Mathematics Sciences • Background of the course (Glen) • Focus of the course • Activity example

  18. Research on the Course • Study of how well students were able to move between representations algebraic ideas of slope • Lesh Translation Model Source: http://www.cehd.umn.edu/rationalnumberproject/03_1.html

  19. Questions • Do students show that they understand the algebra better through ability to move between representations? • Is the course implemented according to the vision of the course designers? • Does the course reflect the standards of the MAA, AMATYC and NCTM?

  20. Results-Student Understanding • Students could make meaning of the algebra by using different representations • Explain in writing • Discuss in class • Students could use spreadsheet program technology to generate representations • Students had the greatest difficulty in writing equations, although they could interpret equations into scenarios.

  21. Results-Implementation • Pedagogy • Aligned with course designers vision • Included group work, discussion, use of multiple representations and was student-centered • Taught in lab, computer based • Multiple solution paths • Deviated some in terms of time in class • Subject matter • Integrated stats, computer science and algebra • Optimization not covered as desired

  22. Results-Alignment with Standards • Aligned with NCTM, MAA, AMATYC as summarized by Baxter Hastings et al., 2006 • Active learning • Less skill work • Essential topics • Multiple representations • Discussion • Technology

  23. Other Incidental Findings • Student Attitude Change • “I feel like I’ve learned some algebra but I didn’t realize I was learning it, which is a really a good thing. Because too many times we walk into a situation like this, like I was just deathly afraid of algebra, and didn’t think that I was capable of doing it. And the way that Mr. X has explained it and walked us through it hasn’t even seemed like a problem at all…and there’s more people that feel the same way that I do.” -Student 2

  24. Other Findings (cont.) • Students’ reflection on their work • Reasoning and sense making • Talked about what they did right and wrong • Students found the math applicable • “You deal with figuring out things in everyday life versus just an algebra problem or just something you have out of a textbook, with just x and y and they don’t mean anything.” -Student 2 • Students perceived the course as student-centered • “It’s more of an everyone-included class rather than the teacher up front, preaching to the class. It works really well.” -Student 3

  25. Questions? GLEN RICHGELS grichgels@bemidjistate.edu HEIDI HANSEN hhansen@bemidjistate.edu

More Related